Loading…

Worked solutions

IB Computer Science HL · Paper 3

Computer Science, Higher Level

Session: November 2018
Marks: 30
Duration: 1 hour
Calculator: Not allowed
Questions: 4

Keep your copy of the paper open alongside. We don't reproduce the questions: each part below is labelled to match the November 2018 Global paper, which your school or the IB can provide.

Practice mode

Hide our working until you've had a go.

Questions

Questions 1–4 · 30 marks

Question 1

4 marks

SAE Level 5 autonomous requirements and CNN max-pooling operations

System fundamentals
Modelling and simulation

(a)

2 marks

State the criteria defining SAE Level 5 full driving automation:
1) Full operational execution: The automated driving system executes all dynamic driving tasks (steering, acceleration, braking, obstacle avoidance, and tactical maneuvering) autonomously across all operational environments.
2) Unconstrained conditions and zero human intervention: The vehicle operates in all roadway, geographic, and adverse weather conditions without geofencing restrictions and requires no steering wheel, pedals, or human driver input; if critical component failure occurs, the system brings the vehicle to a safe stop automatically.

Mentor tip

State clearly that Level 5 demands complete automated driving under all roadway and environmental conditions with zero human intervention required.

(b)

2 marks

Define the operation and objective of max-pooling in Convolutional Neural Networks:
1) Operational mechanism: Max-pooling is a downsampling technique that passes a sliding window (receptive field, typically 2x2 with stride 2) across a feature map, extracting strictly the maximum numerical value within each sub-region while discarding all lesser values.
2) Functional purpose: It reduces the spatial dimensions (height and width) of the intermediate representations, drastically slashing computational parameter counts and memory load while imparting translation invariance to detected features.

P_{i, j} = (u, v) \in Ω_{i, j} max (F_{u, v})

Mentor tip

Describe taking the maximum value from a sliding grid window and state its dual benefits: spatial dimensionality reduction and translation invariance.

Question 2

8 marks

Sensor fusion with HD mapping and ethical dimensions of public road testing

Computer organisation
System fundamentals

(a)

4 marks

Outline why autonomous vehicles require both GPS and High-Definition (HD) maps concurrently:
1) Global localization via GPS: GPS provides absolute geographic coordinates (latitude and longitude), establishing the vehicle's approximate positioning within the broader regional transit grid and selecting the appropriate local tile of the HD map.
2) Resolving GPS precision limits: Standard satellite GPS signals suffer from multipath interference and signal degradation in urban corridors, often exhibiting an accuracy tolerance of 2 to 5 meters, which is inadequate for keeping a car safely centered within a 3-meter lane.
3) Centimeter-level contextualization via HD maps: HD maps store rich centimeter-level 3D spatial models containing exact lane boundaries, crosswalk geometries, curb heights, and fixed traffic signage.
4) Predictive trajectory planning: By matching real-time LiDAR point clouds and camera feeds against the prior HD map features, the vehicle achieves sub-decimeter localization and anticipates road curvature and obscured intersections well beyond physical sensor range.

Mentor tip

Explain how coarse global GPS coordinates determine the general location, while fine-grained centimeter-level HD maps provide exact lane and intersection features.

(b)

4 marks

Evaluate the ethical justifications and concerns of conducting autonomous vehicle beta tests on public roads:
Ethical concerns and risks:
- Absence of informed public consent: Pedestrians, cyclists, and other motorists sharing public roadways are involuntarily exposed to risks without having granted explicit consent to participate in software testing.
- Presence of latent defects: Pre-release beta software inevitably contains edge-case bugs and classification anomalies that can cause catastrophic collisions and physical injuries in chaotic real-world environments.
Ethical justifications and societal benefits:
- Substantial long-term accident reduction: Given that human driver error (distraction, fatigue, impairment) accounts for roughly 90% of all traffic fatalities, accelerating autonomous deployment saves thousands of lives over the long term.
- Necessity of real-world training: Neural networks cannot encounter complex environmental variations, rare edge cases, and human behavioral nuances within synthetic simulations alone; testing in real traffic with trained backup safety drivers aboard minimizes net risk.

Mentor tip

Present a balanced ethical debate: contrast unconsenting public exposure to software bugs against the moral imperative to eliminate the 90% of accidents caused by human driver error.

Question 3

6 marks

Convolutional layer mechanics and feature extraction in CNNs

Modelling and simulation

6 marks

Explain the mathematical and computational processing within the convolutional layer of a CNN:
1) Filter structure: The convolutional layer employs a set of learnable kernels (filters), each structured as a 3D matrix of weights whose depth corresponds exactly to the channel depth of the input volume (e.g., depth 3 for RGB image inputs).
2) Sliding convolution: Each filter moves across the height and width of the input plane in predefined spatial increments governed by the stride parameter, covering a local receptive field at each step.
3) Element-wise dot products: At every spatial position, the weights of the filter are multiplied element-wise by the corresponding input pixel intensities, and the products are summed together with an added scalar bias term.
4) Feature map generation: The resulting scalar sum is mapped into a grid cell of the output activation feature map; high positive activations indicate strong statistical presence of the target visual feature (such as a horizontal edge, texture gradient, or circular contour) within that receptive window.
5) Non-linear activation: The resulting values are passed through an element-wise non-linear activation function (such as ReLU, $f (x) = max (0, x)$ ) to introduce non-linear representational capacity into the network.
6) Spatial invariance: Because the identical filter weights are swept across the entire input grid (parameter sharing), the network detects specific features regardless of their spatial location in the visual scene.

S_{i, j} = m \sum n \sum c \sum I_{i + m, j + n, c} \cdot K_{m, n, c} + b

Mentor tip

Walk through filter dimensions, sliding across receptive fields, element-wise multiplication, summation of dot products into feature maps, and parameter sharing for position invariance.

Question 4

12 marks

Architectural evaluation of the Levangerstadt autonomous transport infrastructure

Networks

12 marks

Evaluate the technologies, protocols, and routing algorithms proposed for Levangerstadt's autonomous transit system:
1) Greenfield testing advantage and deep learning models:
- Levangerstadt represents a purpose-built environment where autonomous vehicles can undergo comprehensive validation before citizens populate the town, virtually eliminating pedestrian risk during initial deployment.
- Constraining the geographic operational domain simplifies visual perception models: road signs, lane markers, and infrastructure boundaries follow uniform specifications, drastically reducing unpredictable visual clutter.
2) Embedded infrastructure sensors and telemetry:
- Sensors embedded in roadbeds, curbs, and intersections continuously monitor lane occupancy, surface icing, and localized blockages, pushing real-time hazard data into the transit control plane.
3) Communication protocols (V2V and V2I):
- Vehicle-to-Vehicle (V2V) direct ad-hoc mesh networks broadcast position, speed, and braking telemetry, allowing convoys of vehicles to negotiate lane merges and maintain tight, aerodynamically efficient headways.
- Vehicle-to-Infrastructure (V2I) protocols interface with smart intersection controllers, dynamically negotiating right-of-way priorities to eliminate conventional traffic lights and avoid deadlocks.
4) High-Definition 3D spatial mapping:
- The contained perimeter allows exhaustive LiDAR and photogrammetric surveying to produce millimeter-precise HD maps. Autonomous vehicles reference this static prior to plan trajectories with minimal compute expenditure.
5) Comparative analysis of pathfinding algorithms:
- Taxis and Dijkstra's algorithm: Dijkstra's single-source shortest path algorithm computes mathematically optimal point-to-point routes between passenger pickup and drop-off intersections. When congestion or roadwork occurs, the central dispatcher updates edge weights dynamically. However, Dijkstra's computational complexity scales as $O ((V + E) lo g V)$ , which can become taxing under large node networks and high dispatch frequencies.
- Buses and the Nearest-Neighbor heuristic: The bus network utilizes the nearest-neighbor greedy heuristic to construct circular multi-stop tours linking required transit points. While exceptionally fast ( $O (V^{2})$ ), nearest neighbor frequently yields suboptimal paths and can leave an excessively long final leg returning to the depot, or fail entirely if topological obstacles isolate vertices.
6) Critical evaluation and synthesis:
- While high-density sensor grids, V2X protocols, and HD maps give Levangerstadt exceptional technical viability, project resilience hinges on managing algorithmic edge cases, providing computational fallbacks when greedy routes fail, and maintaining secure cryptographic authentication across all wireless V2X channels to prevent adversarial traffic spoofing.

O ((V + E) lo g V) vs. O (V^{2})

Mentor tip

Analyze the purpose-built town setting, V2V/V2I wireless protocols, embedded roadbed sensors, compare Dijkstra (optimal point-to-point) against Nearest-Neighbor (greedy tour heuristic), and conclude on algorithmic scaling and security.

Our analysis

Where the marks are

Each part sorted by the topic it mostly tests. Networks carries the most marks on this paper.

Networks12 marks · 40%
Q4
Modelling and simulation8 marks · 27%
Q1, Q3
System fundamentals6 marks · 20%
Q1, Q2
Computer organisation4 marks · 13%
Q2

Mentor insights

Traps to watch for

01
Confusing SAE Level 4 and Level 5 automation · Q1
Level 4 is restricted by geographic operational design domains (geofencing) or specific weather conditions; Level 5 must perform all driving tasks under all roadway and environmental conditions anywhere without human controls.
02
Assuming GPS is sufficiently accurate on its own for lane-keeping · Q2
Standard civilian GPS precision is limited to several meters; autonomous lane-keeping requires centimeter-level precision achieved only by combining GPS with onboard LiDAR and high-density 3D maps.
03
Confusing convolution with a standard matrix multiplication · Q3
The convolution operation involves sweeping a smaller multi-channel filter across spatial sub-regions to compute local element-wise dot products and sum them, rather than multiplying two full matrices together.

Solutions and tips are GeorgeTheTutor's own; the questions are not reproduced here. Not affiliated with or endorsed by the International Baccalaureate Organization.

Want someone to go through your paper with you?

Our maths mentors took these exams recently. One-to-one, they'll find where your marks are going and fix it before May.

Find your maths mentor More past papers

Worked solutions

IB Computer Science HL · Paper 3

Computer Science, Higher Level

Session: November 2018
Marks: 30
Duration: 1 hour
Calculator: Not allowed
Questions: 4

Q1 Q2 Q3 Q4

Keep your copy of the paper open alongside. We don't reproduce the questions: each part below is labelled to match the November 2018 Global paper, which your school or the IB can provide.

Practice mode

Hide our working until you've had a go.

Questions

Questions 1–4 · 30 marks

Question 1

4 marks

SAE Level 5 autonomous requirements and CNN max-pooling operations

System fundamentals
Modelling and simulation

(a)

2 marks

State the criteria defining SAE Level 5 full driving automation:
1) Full operational execution: The automated driving system executes all dynamic driving tasks (steering, acceleration, braking, obstacle avoidance, and tactical maneuvering) autonomously across all operational environments.
2) Unconstrained conditions and zero human intervention: The vehicle operates in all roadway, geographic, and adverse weather conditions without geofencing restrictions and requires no steering wheel, pedals, or human driver input; if critical component failure occurs, the system brings the vehicle to a safe stop automatically.

Mentor tip

State clearly that Level 5 demands complete automated driving under all roadway and environmental conditions with zero human intervention required.

(b)

2 marks

Define the operation and objective of max-pooling in Convolutional Neural Networks:
1) Operational mechanism: Max-pooling is a downsampling technique that passes a sliding window (receptive field, typically 2x2 with stride 2) across a feature map, extracting strictly the maximum numerical value within each sub-region while discarding all lesser values.
2) Functional purpose: It reduces the spatial dimensions (height and width) of the intermediate representations, drastically slashing computational parameter counts and memory load while imparting translation invariance to detected features.

P_{i, j} = (u, v) \in Ω_{i, j} max (F_{u, v})

Mentor tip

Describe taking the maximum value from a sliding grid window and state its dual benefits: spatial dimensionality reduction and translation invariance.

Question 2

8 marks

Sensor fusion with HD mapping and ethical dimensions of public road testing

Computer organisation
System fundamentals

(a)

4 marks

Outline why autonomous vehicles require both GPS and High-Definition (HD) maps concurrently:
1) Global localization via GPS: GPS provides absolute geographic coordinates (latitude and longitude), establishing the vehicle's approximate positioning within the broader regional transit grid and selecting the appropriate local tile of the HD map.
2) Resolving GPS precision limits: Standard satellite GPS signals suffer from multipath interference and signal degradation in urban corridors, often exhibiting an accuracy tolerance of 2 to 5 meters, which is inadequate for keeping a car safely centered within a 3-meter lane.
3) Centimeter-level contextualization via HD maps: HD maps store rich centimeter-level 3D spatial models containing exact lane boundaries, crosswalk geometries, curb heights, and fixed traffic signage.
4) Predictive trajectory planning: By matching real-time LiDAR point clouds and camera feeds against the prior HD map features, the vehicle achieves sub-decimeter localization and anticipates road curvature and obscured intersections well beyond physical sensor range.

Mentor tip

Explain how coarse global GPS coordinates determine the general location, while fine-grained centimeter-level HD maps provide exact lane and intersection features.

(b)

4 marks

Evaluate the ethical justifications and concerns of conducting autonomous vehicle beta tests on public roads:
Ethical concerns and risks:
- Absence of informed public consent: Pedestrians, cyclists, and other motorists sharing public roadways are involuntarily exposed to risks without having granted explicit consent to participate in software testing.
- Presence of latent defects: Pre-release beta software inevitably contains edge-case bugs and classification anomalies that can cause catastrophic collisions and physical injuries in chaotic real-world environments.
Ethical justifications and societal benefits:
- Substantial long-term accident reduction: Given that human driver error (distraction, fatigue, impairment) accounts for roughly 90% of all traffic fatalities, accelerating autonomous deployment saves thousands of lives over the long term.
- Necessity of real-world training: Neural networks cannot encounter complex environmental variations, rare edge cases, and human behavioral nuances within synthetic simulations alone; testing in real traffic with trained backup safety drivers aboard minimizes net risk.

Mentor tip

Present a balanced ethical debate: contrast unconsenting public exposure to software bugs against the moral imperative to eliminate the 90% of accidents caused by human driver error.

Question 3

6 marks

Convolutional layer mechanics and feature extraction in CNNs

Modelling and simulation

6 marks

Explain the mathematical and computational processing within the convolutional layer of a CNN:
1) Filter structure: The convolutional layer employs a set of learnable kernels (filters), each structured as a 3D matrix of weights whose depth corresponds exactly to the channel depth of the input volume (e.g., depth 3 for RGB image inputs).
2) Sliding convolution: Each filter moves across the height and width of the input plane in predefined spatial increments governed by the stride parameter, covering a local receptive field at each step.
3) Element-wise dot products: At every spatial position, the weights of the filter are multiplied element-wise by the corresponding input pixel intensities, and the products are summed together with an added scalar bias term.
4) Feature map generation: The resulting scalar sum is mapped into a grid cell of the output activation feature map; high positive activations indicate strong statistical presence of the target visual feature (such as a horizontal edge, texture gradient, or circular contour) within that receptive window.
5) Non-linear activation: The resulting values are passed through an element-wise non-linear activation function (such as ReLU, $f (x) = max (0, x)$ ) to introduce non-linear representational capacity into the network.
6) Spatial invariance: Because the identical filter weights are swept across the entire input grid (parameter sharing), the network detects specific features regardless of their spatial location in the visual scene.

S_{i, j} = m \sum n \sum c \sum I_{i + m, j + n, c} \cdot K_{m, n, c} + b

Mentor tip

Walk through filter dimensions, sliding across receptive fields, element-wise multiplication, summation of dot products into feature maps, and parameter sharing for position invariance.

Question 4

12 marks

Architectural evaluation of the Levangerstadt autonomous transport infrastructure

Networks

12 marks

Evaluate the technologies, protocols, and routing algorithms proposed for Levangerstadt's autonomous transit system:
1) Greenfield testing advantage and deep learning models:
- Levangerstadt represents a purpose-built environment where autonomous vehicles can undergo comprehensive validation before citizens populate the town, virtually eliminating pedestrian risk during initial deployment.
- Constraining the geographic operational domain simplifies visual perception models: road signs, lane markers, and infrastructure boundaries follow uniform specifications, drastically reducing unpredictable visual clutter.
2) Embedded infrastructure sensors and telemetry:
- Sensors embedded in roadbeds, curbs, and intersections continuously monitor lane occupancy, surface icing, and localized blockages, pushing real-time hazard data into the transit control plane.
3) Communication protocols (V2V and V2I):
- Vehicle-to-Vehicle (V2V) direct ad-hoc mesh networks broadcast position, speed, and braking telemetry, allowing convoys of vehicles to negotiate lane merges and maintain tight, aerodynamically efficient headways.
- Vehicle-to-Infrastructure (V2I) protocols interface with smart intersection controllers, dynamically negotiating right-of-way priorities to eliminate conventional traffic lights and avoid deadlocks.
4) High-Definition 3D spatial mapping:
- The contained perimeter allows exhaustive LiDAR and photogrammetric surveying to produce millimeter-precise HD maps. Autonomous vehicles reference this static prior to plan trajectories with minimal compute expenditure.
5) Comparative analysis of pathfinding algorithms:
- Taxis and Dijkstra's algorithm: Dijkstra's single-source shortest path algorithm computes mathematically optimal point-to-point routes between passenger pickup and drop-off intersections. When congestion or roadwork occurs, the central dispatcher updates edge weights dynamically. However, Dijkstra's computational complexity scales as $O ((V + E) lo g V)$ , which can become taxing under large node networks and high dispatch frequencies.
- Buses and the Nearest-Neighbor heuristic: The bus network utilizes the nearest-neighbor greedy heuristic to construct circular multi-stop tours linking required transit points. While exceptionally fast ( $O (V^{2})$ ), nearest neighbor frequently yields suboptimal paths and can leave an excessively long final leg returning to the depot, or fail entirely if topological obstacles isolate vertices.
6) Critical evaluation and synthesis:
- While high-density sensor grids, V2X protocols, and HD maps give Levangerstadt exceptional technical viability, project resilience hinges on managing algorithmic edge cases, providing computational fallbacks when greedy routes fail, and maintaining secure cryptographic authentication across all wireless V2X channels to prevent adversarial traffic spoofing.

O ((V + E) lo g V) vs. O (V^{2})

Mentor tip

Our analysis

Where the marks are

Each part sorted by the topic it mostly tests. Networks carries the most marks on this paper.

Networks12 marks · 40%
Q4
Modelling and simulation8 marks · 27%
Q1, Q3
System fundamentals6 marks · 20%
Q1, Q2
Computer organisation4 marks · 13%
Q2

Mentor insights

Traps to watch for

01
Confusing SAE Level 4 and Level 5 automation · Q1
Level 4 is restricted by geographic operational design domains (geofencing) or specific weather conditions; Level 5 must perform all driving tasks under all roadway and environmental conditions anywhere without human controls.
02
Assuming GPS is sufficiently accurate on its own for lane-keeping · Q2
Standard civilian GPS precision is limited to several meters; autonomous lane-keeping requires centimeter-level precision achieved only by combining GPS with onboard LiDAR and high-density 3D maps.
03
Confusing convolution with a standard matrix multiplication · Q3
The convolution operation involves sweeping a smaller multi-channel filter across spatial sub-regions to compute local element-wise dot products and sum them, rather than multiplying two full matrices together.

Solutions and tips are GeorgeTheTutor's own; the questions are not reproduced here. Not affiliated with or endorsed by the International Baccalaureate Organization.

Want someone to go through your paper with you?

Our maths mentors took these exams recently. One-to-one, they'll find where your marks are going and fix it before May.

Find your maths mentor More past papers